Let us now begin with the descriptive project, seeking to understand what exactly physicists working in the process matrix research programme mean by their use of causal terminology. To do this, we will examine the discussion around an experiment known as the quantum SWITCH, which is a causally non-separable but still causal process originally proposed as an example of indefinite causal structure in the process matrix formalism[1]}, [2]}. In this process, we use a control qubit to determine the order in which two gates \(A\) , \(B\)  are applied to some other qubit: if the control qubit is in the state \(| 0 \rangle \)  the gate \(A\)  is applied first and the gate \(B\)  follows, whereas if the control qubit is in the state \(| 1 \rangle \)  the gate \(B\)  is applied first and the gate \(A\)  follows. Evidently then if the control qubit is prepared in a superposition of the state \(| 0 \rangle \)  and the state \(| 1 \rangle \)  we will get a superposition of two orderings - in one branch the gates will be applied in the order \(A, B\)  and in the other the gates will be applied in the order \(B, A\) . This scenario is interesting particularly because it can be implemented with current technology, thus it has already been demonstrated in the lab[2]}.
